Solving Combinational Optimization Problems With Evolutionary Single-Pixel Imaging

In this paper, an evolutionary single-pixel imaging (SPI) scheme is proposed to solve combinational optimization problems. SPI is a unique optical imaging technique by replacing the pixelated sensor array in a conventional camera with a single-pixel detector. SPI is conventionally employed for capturing object images or performing image processing tasks. It is a novel attempt to leverage SPI for processing other types of data in addition to images. An Ising machine model is implemented optically with SPI for solving two combinational optimization problems including number partition and graph maximum cut. The binary illumination patterns are encoded based on the spinning states of all the elements and the object image pixel values are encoded to be proportional to the pairwise weighting factors. As the mathematical inner product between object image and illumination pattern, the recorded single-pixel intensity values simulate the Hamiltonian function values. In each iteration, the feedback of single-pixel values is used to update the illumination patterns by selection, crossover and mutation. As the illumination patterns are evolving, an optimal solution of the Hamiltonian function can be finally obtained by our proposed optoelectronic Ising machine scheme.